On the Determining Number and the Metric Dimension of Graphs

José Cáceres, Delia Garijo, María Luz Puertas, Carlos Seara

Abstract

This paper initiates a study on the problem of computing the difference between the metric dimension and the determining number of graphs. We provide new proofs and results on the determining number of trees and Cartesian products of graphs, and establish some lower bounds on the difference between the two parameters.